What Osage Outlaw, bow 101, Corius, and Bubbles, said. It is the stiffness of the shaft, versus the strength of the bow. When the arrow is shot from a bow, it does not just go "straight as an arrow", it first flexes, or bends. The weaker the spine, vs. the strength of the bow, the more bend, or flex, and more time, distance, etc. it takes for the arrow to recover, and fly straight. This where the fletching comes into being important, as it helps the shaft to recover. The more the spine weight, and the bow weight, or strength, are matched, the better the flight, as the arrow recovers quicker. This is more pronounced in an off hand bow, than a center shot, or bow with a shelf, as the arrow has to bend around the bow, "AND" recover. Also the natural arrow shaft material, has a strong side, and a weak side. The strong side goes against the bow, and it is that side that is measured for spine. Anyway, that is "MY" understanding of it. The more your arrows, match in spine, and shaft weight, and length, the better and more consistent your grouping will be. Which is why a lot great bowers, prefer making bows to arrows, and would rather buy, or trade for them, from those who like to make arrows.
A lot of work goes into making the arrows. A lot more variables to consider. I hope this, along with what the others have said can clarify it for you.
Wayne